Home About us Contact
|
Home About us Contact | ||
|
|
||
Fracture Mechanics Problems (fracture + mechanic_problem)
Selected AbstractsThe perturbation method and the extended finite element method.FATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 8 2006An application to fracture mechanics problems ABSTRACT The extended finite element method has been successful in the numerical simulation of fracture mechanics problems. With this methodology, different to the conventional finite element method, discretization of the domain with a mesh adapted to the geometry of the discontinuity is not required. On the other hand, in traditional fracture mechanics all variables have been considered to be deterministic (uniquely defined by a given numerical value). However, the uncertainty associated with these variables (external loads, geometry and material properties, among others) it is well known. This paper presents a novel application of the perturbation method along with the extended finite element method to treat these uncertainties. The methodology has been implemented in a commercial software and results are compared with those obtained by means of a Monte Carlo simulation. [source] Lower and upper bound estimation of isotropic and orthotropic fracture mechanics problems using elements with rotational degrees of freedomINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2008Antoinette de Klerk Abstract We use Rice's path-independent J integral, as well as its dual, the I* integral, to estimate lower and upper bounds of the stress intensity factor K in linear elastic fracture mechanics problems. The elements used contain rotational degrees of freedom, and are derived from the correct energy principles to guarantee path independence of the integrals. That is, the displacement-based elements used in calculating the J integral are derived from the principle of potential energy; the assumed stress elements used in calculating the I* integral are derived from complementary energy principles. For lower bound estimation in particular, elements with drilling degrees of freedom are advantageous, due to their superior accuracy. Numerical results are presented for isotropic and orthotropic mode I and mode II fracture mechanics problems. In addition, we reflect on suitable finite element integration schemes, and applicable values for the problem dependent penalty parameter , which is used in deriving the elements. Copyright © 2006 John Wiley & Sons, Ltd. [source] Boundary element formulation for 3D transversely isotropic cracked bodiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004M. P. Ariza Abstract The boundary traction integral representation is obtained in elasticity when the classical displacement representation is differentiated and combined according to Hooke's law. The use of both traction and displacement integral representations leads to a mixed (or dual) formulation of the BEM where the discretization effort for crack problems is much smaller than in the classical formulation. A boundary element analysis of three-dimensional fracture mechanics problems of transversely isotropic solids based on the mixed formulation is presented in this paper. The hypersingular and strongly singular kernels appearing in the formulation are regularized by using two terms of the displacement series expansion and one term of the traction expansion, at the collocation point. All the remaining integrals are analytically evaluated or transformed by means of Stokes' theorem into regular or weakly singular integrals, which are numerically computed. The method is general and can be used for elements of any shape including quarter-point crack front elements. No change of co-ordinates is required for the integration. The formulation as presented in this paper is something as clear, general and easy to handle as the classical BE formulation. It is used in combination with three-dimensional quadratic and quarter-point elements to obtain accurate results for several different crack problems. Cracks in boundless and finite transversely isotropic domains are studied. The meshes are simple and include only discretization of the crack and the external boundary. The obtained results are in good agreement with those existing in the literature. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||